(a) Operated device and  (b) applied voltage versus normalized coupling efficiency and moving heights.

Finite-Difference Modeling of Dielectric Waveguides with Slanted Facets

Y.-P Chiou, Y.-C. Chiang, C.-H. Lai, C.-H. Du, and H.-C. Chang

Graduate Institute of Photonics and Optoelectronics, National Taiwan University

台湾大学光电所邱奕鹏教授

　 Abstract -- With the help of an improved finite-difference (FD) formulation, we investigate the propagation characteristics of a slant-faceted polarization converter. The formulation is full-vectorial and it takes into consideration discontinuities of fields and their derivatives across the abrupt interfaces. Hence, the limitations in conventional FD formulation are alleviated. Field behaviors across the slanted facet are incorporated in the formulation and hence the staircase approximation in conventional FD formulation is removed to get better modeling of the full-vectorial properties.

　One limitation of conventional finite-difference method is that grids in the computation are normally parallel to the axes in the discretization of field components. Staircase approximation is often required when the fields are cross a slanted interface between two different materials. The convergence is slow due to the staircase approximation as compared to other methods without staircase approximation, e.g. finite-element method. In addition, the full-vectorial properties may not be accurately modeled under such approximation. To get rid of such limitation, our improved finite-difference method is adopted.

　The investigated structure is shown in Fig.1. An x-polarized field is launched from a standard input waveguide (IW). This incident field excites both the first and second hybrid modes of nearly equal modal amplitudes. As these two hybrid modes propagate along the polarization rotating waveguide (PRW), they would become out of phase at the half-beat length and their combined modal fields produce mainly a y-polarized field in the following output waveguide (OW). The polarization rotating waveguideis based on a rib waveguide with one side wall slanted at an angle around 45 degrees.

　In the structure, both hybrid modes have comparable field components in x- and y- directions, and their polarizations are no longer mainly in the x- or y- direction but in the direction parallel or perpendicular to the slanted wall. As shown in Fig.2, the field is periodically converted between x- and y- polarizations. To verify our simulation, finite-element method (FEM) and Yee-mesh-based finite-difference beam propagation method (Yee-FD-BPM) are adopted as shown in Table I. Both electrical and magnetic fields are used at the same time in the formulation of Yee-FD-BPM. Different methods show very good agreement. Furthermore, we also use conventional finite-difference scheme with staircase approximation and index-average approximation to calculate the same problem. We find that the hybrid modes can not be correctly obtained either by our codes or by commercial software. The fundamental modes may become x- or y-dominant modes, not as expected. To sum up, our improved finite-difference scheme can easily handle structures with facets that are not parallel to x- or y-axis, which alleviates the limitation in conventional finite-difference method.

Fig.1 (a) Polarization converter (b) Cross-section view.
Fig.2 Power in x- (solid line) and y- (dashed line) polarized fields along the propagation.
Table I

Design and Analysis of Compact Slot Waveguide Directional Coupler-Based Polarization Splitter on Silicon-on-Insulator

Professor Ding-wei Huang

Graduate Institute of Photonics and Optoelectronics, National Taiwan University

台湾大学光电所黄鼎伟教授

　A slot waveguide directional coupler-based polarization splitter on SOI which exhibits excellent polarization splitting behavior for optical signals around 1.55 mm is designed and analyzed. In our design, the silicon photonic wire is covered by air (n_c = 1) and patterned on the buried oxide layer (n_s = 1.444) of the SOI wafer, where the low-refractive-index region (slot region) is sandwiched by high-refractive-index silicon (n_r = 3.474) at 1.55 μm as shown in Fig.1. The schematic layout of the entire device is shown in Fig. 2. The width w and height h of each photonic wire at the slot region is chosen to be 0.21 μm and 0.25 μm; while the width of the slot w_s is set to be 0.2 μm due to the limitation of the fabrication capability. The propagation of light in the directional coupler can be expressed in terms of even and odd modes with effective indices n_e and n_o, which are functions of the waveguides spacing g as shown in Fig. 3. By carefully choosing the spacing g (g = 0.48 μm) between the two waveguides, the coupling length of TE mode L_TE can be twice that of TM mode L_TM, i.e. L_TE /L_TM = 2. Meanwhile the length of the coupling region of the device is chosen to be L = 2L_TM = L_TE, thus the two modes can be successfully separated into 2 different output ports. By using FDTD technique, the electric field intensities of the TE- and TM-polarized modes propagating in the device can be calculated as shown in Fig. 4.

摘要

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